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Alone in Your Dim, Unheated Room You Light One Candle F{ } ^ { \circ } F

question 52

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Alone in your dim, unheated room you light one candle rather than curse the darkness.Disgusted by the mess, you walk directly away from the candle.The temperature (in F{ } ^ { \circ } F ) and illumination (in % of one candle power) decrease as your distance (in feet) from the candle increases.The table below shows this information.  distance(feet)   Temp. (F)  illuminatiou (%) 055100154.585253.575352674506054756643.553\begin{array}{ccc}\text { distance(feet) } & \text { Temp. }(\mathbf{F}) & \begin{array}{c}\text { illuminatiou } \\(\%) \end{array} \\0 & 55 & 100 \\1 & 54.5 & 85 \\2 & 53.5 & 75 \\3 & 52 & 67 \\4 & 50 & 60 \\5 & 47 & 56 \\6 & 43.5 & 53\end{array}
You are cold when the temperature is below 40°F.You are in the dark when the illumination is at most 50% of one candle power.Suppose you know that at 6 feet the instantaneous rate of change of the temperature is -4.5° F/ft and the instantaneous rate of change of illumination is -3% candle power/ft.Are you in the dark before you are cold, or cold before you are dark?

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